Brighton is one of many "subsidy publishers" that offers to publish your books after you invest a percentage of the publishing costs (in their case 15%). This amount can be substantial and this type of contract isn't recommended for new authors.
Brighton also offers traditional royalty publishing. They pay all the upfront publishing costs and the author receives royalties on all sales. This amount can be miniscule, but this option is better for new authors.
You will end up responsible for more of your own publicity with royalty publishing.
Brighton titles are poorly marketed in either case and if you check out a few you probably won't recognize them as established authors, but that doesn't mean you shouldn't give it a go with Brighton. Any publisher will expect you to sell your own product, especially as a new writer. Except for a few unusual cases, publishing is like any other self-employment--you get what you put into it. Sell yourself, sell your genre and you'll sell your book.
New writers tend to think that their first book will open the door to other opportunities. In reality, it's more like the third or fourth book that opens the door, so keep writing and spam out those manuscripts! Buy a copy of this year's Writer's Market and use it; it's a great resource. Don't dwell on rejection letters (you'll get a lot of them). Don't worry about publishers who never get back to you (many won't). Don't pay anyone to publish your writing (that's like paying your boss to work for him). Don't quit your day job. Don't give up.
Good luck!